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Velocity-Time Graphs (AQA GCSE Physics: Combined Science)
Revision Note
Gradient of a Velocity-Time Graph
- A velocity-time graph shows how the velocity of a moving object varies with time
- The red line represents an object with increasing velocity
- The green line represents an object with decreasing velocity
Increasing and decreasing velocity represented on a velocity-time graph
Acceleration on a Velocity-Time Graph
- Velocity-time graphs also show the following information:
- If the object is moving with a constant acceleration/deceleration
- The magnitude of the acceleration/deceleration
- A straight line represents constant acceleration
- The slope of the line represents the magnitude of acceleration
- A steep slope means large acceleration (or deceleration) - i.e. the object's speed changes very quickly
- A gentle slope means small acceleration (or deceleration) - i.e. the object's speed changes very gradually
- A flat line means the acceleration is zero - i.e. the object is moving with a constant velocity
Interpreting the slope of a velocity-time graph
Calculating the Gradient of a Velocity-Time Graph
- The acceleration of an object can be calculated from the gradient of a velocity-time graph
The gradient of a velocity-time graph can be found by dividing the change in velocity by the change in time
Worked example
A cyclist is training for a cycling tournament.
The velocity-time graph below shows the cyclist's motion as they cycle along a flat, straight road.
(a) In which section (A, B, C, D, or E) of the velocity-time graph is the cyclist's acceleration the largest?
(b) Calculate the cyclist's acceleration between 5 and 10 seconds.
Answer:
Part (a)
Step 1: Recall that the slope of a velocity-time graph represents the magnitude of acceleration
- The slope of a velocity-time graph indicates the magnitude of acceleration
Therefore, the only sections of the graph where the cyclist is accelerating are sections B and D
- Sections A, C, and E are flat; in other words, the cyclist is moving at a constant velocity (therefore, not accelerating)
Step 2: Identify the section with the steepest slope
- Section D of the graph has the steepest slope
-
Hence, the largest acceleration is shown in section D
Part (b)
Step 1: Recall that the gradient of a velocity-time graph gives the acceleration
- Calculating the gradient of a slope on a velocity-time graph gives the acceleration for that time period
Step 2: Draw a large gradient triangle at the appropriate section of the graph
- A gradient triangle is drawn for the time period between 5 and 10 seconds
Step 3: Calculate the size of the gradient and state this as the acceleration
- The acceleration is given by the gradient, which can be calculated using:
- Therefore, the cyclist accelerated at 1 m/s2 between 5 and 10 seconds
Examiner Tip
Use the entire slope, where possible, to calculate the gradient. Examiners tend to award credit if they see a large gradient triangle used.
Remember to actually draw the lines directly on the graph itself, particularly when the question asks you to use the graph to calculate the acceleration.
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